In p >> n settings, full posterior sampling using existing Markov chain Monte
Carlo (MCMC) algorithms is highly inefficient and often not feasible from a practical
perspective. To overcome this problem, we propose a scalable stochastic search algorithm that is called the Simplified Shotgun Stochastic Search (S5) and aimed at rapidly explore interesting regions of model space and finding the maximum a posteriori(MAP) model. Also, the S5 provides an approximation of posterior probability of each model (including the marginal inclusion probabilities). This algorithm is a part of an article titled "Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-dimensional Settings" (2018) by Minsuk Shin, Anirban Bhattacharya, and Valen E. Johnson and "Nonlocal Functional Priors for Nonparametric Hypothesis Testing and High-dimensional Model Selection" (2020+) by Minsuk Shin and Anirban Bhattacharya.